Use Lagrange multipliers to solve the following exercise. A home
improvement contractor is painting the walls and ceiling of a
rectangular room. The volume of the room is 5346.00 cubic ft. The
cost of wall paint is $0.06 per square foot and the cost of ceiling
paint is $0.11 per square foot. Find the room dimensions that
result in a minimum cost for the paint. length ft width ft height
ft What is the minimum cost for the paint? (Round your answer to
two decimal places.) $